## MOLECULAR BOND STRENGTHS, BOND ENERGIES, AND FORCE CONSTANTS

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### Date

1965

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Ohio State University

### Abstract

``Bond Strength'' is a term which is much used but seldom (if ever) defined. A possible definition would be that the bond strength is the average force S required to do 99.99 per cent of the work necessary to produce infinite separation of the atoms X and Y in the $X-Y$ bond. That is ""[FIGURE]"" \begin{equation}S= \int^{R}_{r_{v}} f(r)\ dr/ \int^{R}_{r_{e}}dr,\end{equation} where $f(r)$ is the force at the internuclear separation $r_{i} r_{e}$ is the separation at equilibrium, and R is that value of r at which the potential energy $U_{R}=0.9999 W_{De} W_{De}$ being the dissociation energy (or bond energy). Using the Morse potential energy function, with $U_{R}=0.9999 W_{De}$ and $r=R$, one finds that $R - r_{e}=9.900/a$, where a is the constant in the Morse function that determines the curvature of the potential energy curve near $r_{v}$. Using this, and replacing the first integral in Eq. (1) by 0.9999 $W_{De}$, gives \begin{equation}S=0.1010\ a\ W_{De}\end{equation} If a is not known, one can use the stretching force constant f for the X-Y bond. This is given by $f=d^{2}U/dr^{2}=2 a^{2} W_{De}$. Using the value of a obtained from this, Eq. (2) becomes \begin{equation}S=0.07142 (f\ W_{De})^{1/2},\end{equation} or \begin{equation}S=9.0419\ \mu\ dyn (f\ W_{De})^{1/2}\end{equation} when f is in microdynes per picometer and $W_{De}$ is in electron-volts. Previously, L. Pokras obtained for $f, W_{De}$, the values $51.211 \mu$ dyn/pm, 5.2933 eV, for $HCl^{35}$, and 51.194, 5.3211, for $HCl^{37}$. Using these, $S(HCl^{35})=148.88$ and $S(HCl^{37})=149.24 \mu dyn$. Values of S for other bonds, calculated from less reliable values of $W_{De}$ are: $CO 385; N_{2} 370; C=C 335;C=C 221; NO 263; O_{2} 221; OH 167; H_{2} 138; NH 133; CH 132; C-C 115; Cl_{2} 82; Br_{2} 62; I_{2} 46; Li_{2} 15; Na_{2} 10;$ and $K_{2} 6 \mu {\rm dyn}$. It is interesting to note that the S values of $C-C, C=C$, and $C=C$ are in the ratio 1 to 1.9 to 2.9.

### Description

Author Institution: Physics Department, Illinois Institute of Technology